Catalan numbers: Difference between revisions

=={{header|AutoHotkey}}==

As AutoHotkey has no BigInt, the formula had to be tweaked to prevent overflow. It still fails after n=22

<lang AHK>Loop 15

out .= "`n" Catalan(A_Index)

Msgbox % clipboard := SubStr(out, 2)

catalan( n ) {

; By [VxE]. Returns ((2n)! / ((n + 1)! * n!)) if 0 <= N <= 22 (higher than 22 results in overflow)

If ( n < 3 ) ; values less than 3 are handled specially

Return n < 0 ? "" : n = 0 ? 1 : n

i := 1 ; initialize the accumulator to 1

Loop % n - 1 >> 1 ; build the numerator by multiplying odd values between 2N and N+1

i *= 1 + ( n - A_Index << 1 )

i <<= ( n - 2 >> 1 ) ; multiply the numerator by powers of 2 according to N

Loop % n - 3 >> 1 ; finish up by (integer) dividing by each of the non-cancelling factors

i //= A_Index + 2

Return i

}</lang>

Output:

<pre>1

2

5

14

42

132

429

1430

4862

16796

58786

208012

742900

2674440

9694845</pre>